which is simply a flat prior for \(\beta _1\)  and an exponential prior for \(e^{\beta _0}\)  with scale \(\hat{b} = \exp (\hat{\beta }_0 + \gamma )\) , where \(\hat{\beta }_0\)  is the maximum likelihood estimator and \(\gamma \approx 0.5772\)  is Euler's constant. This default prior is used here, rather than, say, the Pólya–gamma prior of [1]}, because embedding its more sophisticated posterior sampling scheme inside the learning rate selection procedures was simply too expensive.
